Neutron powder-diffraction measurements have been performed on polycrystalline lithium and sodium specimens at 80 and 20 K and on potassium metal at 80 and 10 K. Lithium is bcc (body-centered cubic) at room temperature and undergoes a martensitic structural phase transformation to a 9R (samarium-type) form at low temperature. This experiment presents evidence that the 9R phase is present in sodium as well as lithium. No evidence of a transformation was observed in potassium at 10 K. The diffraction lines for both lithium and sodium after the phase transformation exhibit position shifts and broadening characteristic of stacking-fault defects. The line shifts, line broadening, and transformed fraction for the low-temperature phase of lithium and sodium metal are reported. The diffraction peak position shifts are, however, different from those predicted for deformation-type stacking faults alone. Qualitative agreement of the experimental results with stacking-fault-model calculations was obtained for a ``double-twin'' type of layer defect.